If xAy means x+y, xSy means x-y, xMy means `(x)xxy` and xDy means `xdivy`. Then the value of 4D2S3M6A12 is :

Options

A. -4
B. 18
C. `(-47)/4`
D. none of these

Answer

To solve the expression \( 4D2S3M6A12 \), we need to decode the operations based on the definitions provided:

- \( xAy \) means \( x + y \)
- \( xSy \) means \( x - y \)
- \( xMy \) means \( x \times y \)
- \( xDy \) means \( x \div y \)

Now, let's break down the expression step by step.

### Step 1: Decode the Expression
The expression \( 4D2S3M6A12 \) can be rewritten using the definitions:
- \( 4D2 \) means \( 4 \div 2 \)
- \( S3 \) means \( -3 \)
- \( M6 \) means \( \times 6 \)
- \( A12 \) means \( + 12 \)

So, we can rewrite the expression as:
\[ (4 \div 2) - 3 \times 6 + 12 \]

### Step 2: Perform Division
First, we perform the division:
\[ 4 \div 2 = 2 \]

Now, substitute this back into the expression:
\[ 2 - 3 \times 6 + 12 \]

### Step 3: Perform Multiplication
Next, we perform the multiplication:
\[ 3 \times 6 = 18 \]

Now, substitute this back into the expression:
\[ 2 - 18 + 12 \]

### Step 4: Perform Subtraction
Now, we perform the subtraction:
\[ 2 - 18 = -16 \]

Now, substitute this back into the expression:
\[ -16 + 12 \]

### Step 5: Perform Addition
Finally, we perform the addition:
\[ -16 + 12 = -4 \]

### Final Answer
Thus, the value of \( 4D2S3M6A12 \) is:
\[ \boxed{-4} \]